A. Pultr, W. Tholen
abstract:
The notion of Quillen factorization system is obtained by strengthening the
left and right lifting properties in a Quillen model category to the unique
diagonalization property. An equivalent description of this notion is given in
terms of a double factorization system which decomposes each arrow uniquely into
three factors. The free category with Quillen factorization system over a given
category is described.